Problem with Talmi Transformation

[magnificat]

I'm trying to calculate the Talmi transformation of two 3d harmonic oscillator wavefunctions in spherical coordinates with the quantum numbers: n1=0, l1=1, n2=0, l2=1.

For some reason, every time I do it I end up with extra terms.

The formula I am using (from several textbooks) is: Psi(r1)*Psi(r2)=Ʃ<n1 l1 n2 l2 λ
|n l N L λ><l1 m1 l2 m2|λ 0><l m L M|λ 0>*Psi(r)*Psi(R)

where r=(r1-r2)/√2; R=(r1+r2)/√2

I have the 0 as my value for μ, and this is guaranteed to always be true. Is this the right way to do this transformation?

I have attached a Mathematica notebook with my test case.

 

[azntoon]

The answer I'm getting is:Psi(r1)*Psi(r2)=2*Ʃ<n1 l1 n2 l2 λ|n l N L λ><l1 m1 l2 m2|λ 0><l m L M|λ 0>*Psi(r)*Psi(R)+Ʃ<n1 l1 n2 l2 λ|n l N L λ><l1 m1 l2 m2|λ 0>*Psi(r)*Psi(R).The extra terms appear to be coming from the second sum, and I am not sure why they are there. Can anyone help me out?